In given random varaible $ X$ ~ $Geo(p)$ what is E(X=x)?
(I know that E(X)=$\frac{1}{p})$.
2026-04-13 06:05:40.1776060340
In given random varaible $ X$ ~ $Geo(p)$ what is E(X=x)?
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If by $X=x$ you mean indicator $\Bbb{1}(X=x)$, then the answer is merely $$\Bbb{E}(\Bbb{1}(X=x)) = \Bbb{P}(X=x)$$ For natural $x$ the last probability is $p^{x - 1}(1-p)$ or $p^x$ depending on how you define $Geo(p)$ distribution.